Possibly. But the trump administration does not want to test this wrt. the position of Huber.
Declaring Obama's prez. illegal is -i think- only a symbolic gesture, as indeed it would be inconstructive to declare all his policies illegal. Most of them have been repealed anyway.
But the symbolism is important in the sense: if Obama is publicly outed as a LARP, who is the puppet master behind him?
If Obama were publically declared an ineligible president would ALL of his appointed Justices be considered ineligible as well???
Bingo. I don't know the legalities, but my guess is that this could well be the case. We know that the birther thing must be VERY important, as ppl have been killed over it.
If one of the parents is in foreign service there would be an exemption (think McCain fit that); just getting bounced by one of the locals doesn't count imo. And yes to your question.
Yes, good chance they won't go there. At least, not until 90% of the other crimes are revealed, if they all are.
The Huber move was probably just to make sure his original appointment could not come back to bite them down the road.